CXML
duskys
Unsymmetric sparse matrix solve using skyline storage scheme
FORMAT
DUSKYS (n, au, iaudiag, nau, al, ialdiag, nal, bx, ldbx, nbx, iparam,
rparam, iwrk, rwrk, ierror)
Arguments
n integer*4
On entry, the order of the matrix A.
On exit, n is unchanged.
au real*8
On entry, if istore = 1 or 2, au contains the factors
U and D of the L*D*U factorization of the matrix A.
Array AU is of length at least nau, where nau is the
envelope size of the upper triangular part of A,
including the diagonal. If istore = 3, then au
contains the L*D*U factorization of the matrix A. In
this case, array AU is of length at least nau, where
nau is the envelope size of the matrix A. The L*D*U
factorization has been obtained by a prior call to the
routine DUSKYF. au must remain unchanged between
calls to the routines DUSKYF and DUSKYS.
On exit, au is unchanged.
iaudiag integer*4
On entry, an array containing the pointers to the
locations of the diagonal elements in array AU.
iaudiag is of length at least n for the profile-in and
the structurally symmetric profile-in storage modes.
iaudiag is of length at least (n+1) for the diagonal-
out storage mode.
On exit, iaudiag is unchanged.
nau integer*4
On entry, the number of elements stored in array AU.
If istore = 1 or 2, then nau is the envelope size of
the upper triangular part of the matrix A. If istore =
3, then nau is the envelope size of the matrix A. For
the profile-in and the structurally symmetric profile-
in storage modes, nau = IAUDIAG(n). For the
diagonal-out storage mode, nau = IAUDIAG(n+1) - 1.
On exit, nau is unchanged.
al real*8
On entry, if istore = 1 or 2, al contains the factor
L of the L*D*U factorization of the matrix A. Array AL
is of length at least nal, where nal is the envelope
size of the lower triangular part of A, including the
diagonal. If istore = 3, then al is a dummy
argument. The L*D*U factorization is obtained from a
prior call to the routine DUSKYF. al must remain
unchanged between calls to the routines DUSKYF and
DUSKYS.
On exit, al is unchanged.
ialdiag integer*4
On entry, an array containing the pointers to the
locations of the diagonal elements in array AL.
ialdiag is of length at least n for the profile-in
storage mode. ialdiag is of length at least n+1 for
the diagonal-out storage mode. If istore = 3, then
ialdiag is a dummy argument.
On exit, ialdiag is unchanged.
nal integer*4
On entry, the number of elements stored in array AL.
If istore = 1 or 2, then nal is also the envelope size
of the lower triangular part of the matrix A. For the
profile-in storage mode, nal = IALDIAG(n). For the
diagonal-out storage mode, nal = IALDIAG(n+1) - 1. If
istore = 3, then nal is a dummy argument.
On exit, nal is unchanged.
bx real*8
On entry, a two dimensional array BX of order ldbx by
at least nbx, containing the nbx right sides.
On exit, bx contains the solutions for the nbx
systems.
ldbx integer*4
On entry, the leading dimension of array BX. ldbx >=
n.
On exit, ldbx is unchanged.
nbx integer*4
On entry, the number of right sides.
On exit, nbx) is unchanged.
iparam integer*4
An array of length at least 100, containing the integer
parameters for the matrix solve operation.
iparam(1): niparam
On entry, defines the length of the array IPARAM.
niparam >= 100.
On exit, iparam(1) is unchanged.
iparam(2): nrparam
On entry, defines the length of the array RPARAM. As
the real parameter array is not used at present,
nrparam may be unspecified.
On exit, iparam(2) is unchanged.
iparam(3): niwrk
On entry, defines the size of the integer work array,
IWRK. niwrk >=4n.
On exit, iparam(3) is unchanged.
iparam(4): nrwrk
On entry, defines the size of the real work array,
RWRK. As the real work array is not used at present,
nrwrk may be unspecified.
On exit, iparam(4) is unchanged.
iparam(5): iounit
On entry, defines the I/O unit number for printing
error messages and information from the routine DUSKYF.
The I/O unit must be opened in the calling subprogram.
If iounit <= 0, no output is generated.
On exit, iparam(5) is unchanged.
iparam(6): iolevel
On entry, defines the message level that determines the
amount of information printed out to iounit, when
iounit > 0.
iolevel = 0 : fatal error messages only
iolevel = 1 : error messages and minimal information
iolevel = 2 : error messages and detailed information
On exit, iparam(6) is unchanged.
iparam(7): idefault
On entry, defines if the default values should be used
in arrays IPARAM and RPARAM. If idefault = 0, then the
following default values are assigned:
IPARAM(1) = niparam = 100
IPARAM(6) = iolevel = 0
IPARAM(8) = istore = 1
IPARAM(9) = itrans = 0
If idefault = 1, then you must assign values to the
above variables before the call to the DUSKYF routine.
On exit, iparam(7) is unchanged.
iparam(8): istore
On entry, defines the type of storage scheme used for
the skyline matrix. If istore = 1, the unsymmetric
matrix A is stored using the profile-in storage mode;
if istore = 2, the unsymmetric matrix A is stored
using the diagonal-out storage mode; if istore = 3,
the unsymmetric matrix A is stored using the
structurally symmetric profile-in storage mode. The
storage scheme used in the routines DUSKYF and DUSKYS
must be identical. Default: istore = 1.
On exit, iparam(8) is unchanged.
iparam(9): itrans
On entry, defines the form of matrix used in the
solution. If itrans = 0, the system solved is A X =
B; if itrans = 1, the system solved is trans(A) X = B.
Default: itrans = 0.
On exit, iparam(9) is unchanged.
rparam real*8
On entry, an array containing the real parameters for
the solution.
On exit, rparam is unchanged. rparam is not used by
the routine DUSKYS at present, but is reserved for
future use.
iwrk integer*4
On entry, an array of length at least 4n used for
integer workspace. The first 4n elements of the array
IWRK, generated by the routine DUSKYF, should be passed
unchanged to the routine DUSKYS.
On exit, the first 4n elements of iwrk are unchanged.
rwrk real*8
On entry, an array used for real workspace.
On exit, rwrk is unchanged. Presently, rwrk is not
used by the routine DUSKYS, but is reserved for future
use. It can be a dummy variable.
ierror integer*4
On entry, an unspecified variable.
On exit, ierror contains the error flag. A value of
zero indicates a normal exit from the routine DUSKYS.
Description
DUSKYS solves the system
A * X = B
or
trans(A) * X = B
where A is an unsymmetric matrix stored in a skyline form, using either the
profile-in storage mode, the diagonal-out storage mode, or the structurally
symmetric profile-in storage mode; B is a matrix of nbx right sides and X
is the matrix of the corresponding nbx solution vectors. On entry to the
routine DUSKYS, the array BX contains the nbx right sides; on exit, these
are overwritten by the solution vectors. The variable itrans determines
whether the matrix A or trans(A) is used in the solution process.
The matrix A has been factorized as
A = L D U
by a prior call to the routine DUSKYF. L is a unit lower triangular matrix,
U is a unit upper triangular matrix, and D is a diagonal matrix. The first
4n elements of the integer workspace array IWRK, generated by DUSKYF,
contain information for use by DUSKYS and therefore must remain unchanged
between the calls to the routines DUSKYF and DUSKYS. The real work array
RWRK is not used at present. The storage scheme used in the routines
DUSKYF and DUSKYS must be identical.
Once the factorization has been obtained, the routine DUSKYS can be used to
solve a system with multiple right sides, by setting nbx > 1. The routine
can also be called repeatedly, provided the first 4n elements of the work
array IWRK remain unchanged between calls.
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